Tensor product Gauss-Lobatto points are Fekete points for the cube

Tensor products of Gauss-Lobatto quadrature points are frequently used as c ollocation points in spectral element methods. Unfortunately, it is not kno wn if Gauss-Lobatto points exist in non-tensor-pro duct domains like the si mplex. In this work, we show that the n-dimensional tensor-product of Gauss -Lobatto quadrature points are also Fekete points. This suggests a way to g eneralize spectral methods based on Gauss-Lobatto points to non-tensor-prod uct domains, since Fekete points are known to exist and have been computed in the triangle and tetrahedron. In one dimension this result was proved by FeJer in 1932, but the extension to higher dimensions in non-trivial.